Finite Group Databasebeta

← #15634945

Subgroups — #15634945

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082500C211yesmaximal, characteristic, complemented
2#13082492C211yesmaximal, characteristic, complemented
3#13081673C214yesmaximal, complemented
4#13081635C214yesmaximal, complemented
5#13081611C214yesmaximal, complemented
6#13081592C214yesmaximal, complemented
7#13079095C212yesmaximal, complemented
8C2×#10622698C211yesmaximal, characteristic, complemented
9#13078139C212yesmaximal, complemented
10#13078127C212yesmaximal, complemented
11#13078097C211yesmaximal, characteristic, complemented
12#13077546C211yesmaximal, characteristic, complemented
13#13077471C212yesmaximal, complemented
14C4×#67003C211yesmaximal, characteristic, complemented
15C11×#3039C211yesmaximal, characteristic, complemented
16C2×C11×#137C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19#10623361C2212yes—
20C2×#67003C2211yescharacteristic
21#10623347C2212yes—
22#10623343C2212yes—
23C22×#4325C2212yes—
24C22×#4325C2212yes—
25C2×#66961C2212yes—
26#10623263C2214yescomplemented
27#10623262—22no—
28#10623259—22no—
29#10623252C2214yescomplemented
30#10623116C2214yes—
31#10623084C2214yes—
32#10623081—24no—
33#10623066—22no—
34#10623052C2212yes—
35#10623044—24no—
36#10623008—22no—
37C2×#66927C2211yescharacteristic
38C4×#4339C2211yescharacteristic
39#10623001C2211yescharacteristic
40C11×#462C2214yescomplemented
41C11×#461C2214yescomplemented
42C11×#423C2211yescharacteristic
43C11×#419C2212yes—
44#10622846C2211yescharacteristic
45#10622804C2214yescomplemented
46#10622803C2214yescomplemented
47#10622798C2218yescomplemented
48#10622789C2214yescomplemented
49#10622788C2214yescomplemented
50#10622776C2218yescomplemented
51#10622744C2212yes—
52#10622735C2212yes—
53#10622732C2212yes—
54#10622698C2214yes—
55#10622698C2214yes—
56C4×#4326C2212yescomplemented
57C4×#4325C2212yescomplemented
58C4×#4324C2212yescomplemented
59C4×#4323C2212yescomplemented
60#10622615C2211yescharacteristic
61#10622611C2211yescharacteristic
62C2×C4×C11⋊C8C2211yescharacteristic
63#10622461C2214yes—
64#10622456C2214yes—
65#10622444C2214yescomplemented
66#10622443C2214yescomplemented
67#10622432C2218yescomplemented
68#10622431C2218yescomplemented
69#10622430C2218yescomplemented
70#10622401C2218yescomplemented
71C2×C11×#41C2311yescharacteristic
72C22×Q8×C11C2312yes—
73C2×#4339—24no—
74C2×#4339C2311yescharacteristic
75C22×D44—22no—
76C22×D44C2312yes—
77C11×#137—44no—
78C2×C11×Q16C2314yes—
79C2×C11×SD16C2314yes—
80C2×C11×M16C2312yes—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8C2314yes—
84C4×Q8×C11C2312yes—
85C4×D4×C11—22no—
86C4×D4×C11C2312yes—
87C11×#117—21no—
88C11×#117C2311yescharacteristic
89C2×C11×C4⋊C4—22no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92#67003—24no—
93#67000C2314yes—
94#67000C2314yes—
95#66999—24no—
96Q8×Dic11—24no—
97Q8×Dic11C2318yes—
98#66997C2314yes—
99C2×#4326C2311yescharacteristic
100C2×#4325—28no—
101C2×#4325—44no—
102C2×#4325C2314yes—
103C2×#4325C2314yes—
104C2×#4325C2311yescharacteristic
105C2×#4325C2318yes—
106#66993C2314yes—
107#66990—24no—
108C2×#4324C2311yescharacteristic
109C2×#4323C2311yescharacteristic
110#66983—24no—
111#66983—24no—
112#66982—24no—
113C4×C22⋊D11—22no—
114#66979—24no—
115#66979C2311yescharacteristic
116#66979C2312yes—
117#66977D414yes—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120#66961—44no—
121C2×D88C2314yes—
122C2×#4314C2314yes—
123#66951—28no—
124#66950—24no—
125#66947—28no—
126#66946C2318yes—
127#66945—24no—
128#66943—24no—
129#66942—28no—
130#66940—24no—
131#66937—28no—
132C22⋊C4×D11—24no—
133#66928—24no—
134#66927—21no—
135#66927—21no—
136#66927C2314yes—
137C4×D44—24no—
138C4×D44—24no—
139C4×D44C2312yes—
140#66925—21no—
141C42×D11—21no—
142#66923D412yes—
143#66922D412yes—
144C4×Dic22C2312yes—
145C4×Dic22C2314yes—
146C11×C4⋊C8C2314yes—
147C11×#103C2318yes—
148#66899C2312yes—
149#66896C2312yes—
150#66885C2318yes—
151#66879C2314yes—
152Dic11⋊C8C2318yes—
153C8×Dic11C2314yes—
154#66874C2312yes—
155#66873C2312yes—
156#66872C2312yes—
157#66871C2312yes—
158C4×C11⋊C8C2312yes—
159C4×C11⋊C8C2312yes—
160#61410—111nomaximal, Sylow
161C23×D11—22no—
162C11×#41—22no—
163C11×#41—22no—
164C2×Q8×C11—22no—
165C2×Q8×C11—24no—
166C2×Q8×C11—24no—
167C2×Q8×C11C2411yescharacteristic
168C2×Q8×C11C2414yes—
169C2×D4×C11—21no—
170C2×D4×C11C2411yescharacteristic
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—28no—
177C2×C22⋊D11—21no—
178#4339—22no—
179#4339—22no—
180#4339—88no—
181C2×D44—22no—
182C2×D44—24no—
183C2×D44—24no—
184C2×D44—24no—
185C2×D44—24no—
186C2×D44—84no—
187C2×D44C2411yescharacteristic
188C2×D44C2414yes—
189C2×C4×D11—28no—
190C2×C4×D11—21no—
191C2×C4×D11—22no—
192C2×Dic22C2×D414yes—
193C2×Dic22C2411yescharacteristic
194C11×Q16—44no—
195C11×SD16—44no—
196C11×M16—24no—
197C2×C8×C11C2414yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4C2412yes—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—22no—
204C42×C11—21no—
205C42×C11—22no—
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11C2412yes—
209C22⋊Dic11—21no—
210C22⋊Dic11C2×D414yes—
211#4326—22no—
212#4325—28no—
213#4325—28no—
214#4325—22no—
215#4325—48no—
216#4324—22no—
217#4323—22no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4—22no—
222C4⋊Dic11—28no—
223C4⋊Dic11C2×D414yes—
224C4⋊Dic11C2×D414yes—
225C4⋊Dic11C2412yes—
226Dic11⋊C4—28no—
227Dic11⋊C4—22no—
228Dic11⋊C4C2×D418yes—
229C4×Dic11—28no—
230C4×Dic11—22no—
231C4×Dic11—21no—
232C4×Dic11C2414yes—
233C2×C11⋊C8—22no—
234C2×C11⋊C8#4114yescomplemented
235C2×C11⋊C8C2412yes—
236C2×C11⋊C8C2411yescharacteristic
237C2×C11⋊C8C2411yescharacteristic
238D88—44no—
239#4314—44no—
240#3509—111no—
241#3508—111no—
242#3400—114no—
243#3397—114no—
244#3394—114no—
245#3392—114no—
246#3154—112no—
247C2×#492—111no—
248#3043—112no—
249#3042—112no—
250#3039D1111yescharacteristic, complemented
251#3038—111no—
252#2960—111no—
253#2949—112no—
254C4×#135—111no—
255C23×C11—21no—
256C23×C11C22×D411yescharacteristic
257C22×D11—21no—
258C22×D11—24no—
259C22×D11—44no—
260C22×D11—84no—
261Q8×C11—24no—
262Q8×C11—21no—
263Q8×C11—24no—
264Q8×C11—21no—
265Q8×C11—44no—
266D4×C11—21no—
267D4×C11—21no—
268D4×C11—42no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—44no—
274C2×C4×C11—42no—
275C2×C4×C11—44no—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D412yes—
279C2×C4×C11C2×#4112yes—
280C2×C4×C11H(5,𝔽2)12yes—
281C2×C4×C11C2511yescharacteristic
282C22⋊D11—42no—
283C22⋊D11—88no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11C22×D418yes—
287D44—21no—
288D44—24no—
289D44—24no—
290D44—21no—
291D44—44no—
292D44—48no—
293D44—84no—
294C4×D11—42no—
295C4×D11—44no—
296C4×D11—88no—
297Dic22—28no—
298Dic22—21no—
299Dic22—21no—
300C8×C11—24no—
301C11⋊C8—22no—
302C11⋊C8C2×#4112yes—
303C11⋊C8C2×#4112yes—
304C2×#137C2×D1112yes—
305C2×AGL(1,ℤ/8)—112no—
306C2×#135—111no—
307C22×SD16—112no—
308C22×SD16—112no—
309#559—114no—
310#557—114no—
311#556—114no—
312#552—224no—
313#550—114no—
314#546—224no—
315#541—222no—
316#540—222no—
317#536—112no—
318#535—112no—
319#533—111no—
320#533—222no—
321#532—222no—
322C2×C4⋊Q8C2×D1111yescharacteristic
323C2×#127—111no—
324#519—112no—
325#518—112no—
326C4×#41—111no—
327C4×#41C2×D1111yescharacteristic
328#497—114no—
329#496—114no—
330#495—114no—
331#492—114no—
332#492—114no—
333#492—114no—
334#464—118no—
335#463—118no—
336#462C2×D1114yescomplemented
337#461—118no—
338#461C2×D1114yescomplemented
339#460—118no—
340#460—114no—
341#459—114no—
342#446—114no—
343C8×Q8—114no—
344#440—118no—
345C4×Q16—112no—
346C4×SD16—112no—
347C4×SD16—112no—
348C4×SD16—118no—
349C4×D8—112no—
350#427—111no—
351#424—112no—
352#423C2×D1111yescharacteristic
353#419C2×D1112yes—
354#418—112no—
355#416—111no—
356#416—111no—
357#405—112no—
358C2×C4×C8—111no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—42no—
362C22×C11#55012yes—
363C22×C11C23×D411yescharacteristic
364C2×D11—44no—
365C2×D11—41no—
366C2×D11—48no—
367C2×D11—42no—
368C2×D11—164no—
369C4×C11—22no—
370C4×C11—41no—
371C4×C11—44no—
372C4×C11—42no—
373C4×C11#55012yes—
374C4×C11#57714yes—
375C4×C11C22×#4111yescharacteristic
376C4×C11C2×H(5,𝔽2)11yescharacteristic
377Dic11—28no—
378Dic11—41no—
379Dic11—42no—
380C2×#41—111no—
381C2×#41—224no—
382C2×#41C22×D1111yescharacteristic
383C22×Q8C22×D1112yes—
384C22×D4—112no—
385C22×D4—222no—
386#137—44no—
387AGL(1,ℤ/8)—444no—
388#135—224no—
389C2×Q16—111no—
390C2×Q16C22×D1114yes—
391C2×SD16—114no—
392C2×SD16—114no—
393C2×SD16—111no—
394C2×SD16—111no—
395C2×SD16—118no—
396C2×SD16—114no—
397C2×SD16—228no—
398C2×SD16—444no—
399C2×SD16C22×D1114yes—
400C2×D8—111no—
401C2×D8—114no—
402C2×M16C22×D1112yes—
403C22×C8—111no—
404C22×C8—111no—
405C4⋊Q8—21no—
406C4⋊Q8—21no—
407C4⋊Q8—114no—
408C4⋊Q8—112no—
409C4⋊Q8C22×D1114yes—
410#127—114no—
411#127—114no—
412#127—221no—
413#127—221no—
414#126—228no—
415#125—112no—
416#125—224no—
417#125—228no—
418#124—114no—
419#124—114no—
420#124—224no—
421#123—224no—
422#123—228no—
423C22⋊Q8—114no—
424C22⋊Q8—224no—
425C22⋊Q8—224no—
426#121—228no—
427#121—224no—
428#121—224no—
429#120—224no—
430C4×Q8—114no—
431C4×Q8—118no—
432C4×Q8—112no—
433C4×Q8—224no—
434C4×Q8—224no—
435C4×Q8C22×D1112yes—
436C4×D4—22no—
437C4×D4—118no—
438C4×D4—112no—
439C4×D4—224no—
440C4×D4—224no—
441C4×D4—222no—
442C4×D4C22×D1112yes—
443#117—21no—
444#117—112no—
445#117—111no—
446#117—224no—
447#117—224no—
448#117—221no—
449#117C22×D1111yescharacteristic
450C2×C4⋊C4—22no—
451C2×C22⋊C4—224no—
452C2×C42—21no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455#107—112no—
456#106—112no—
457C4⋊C8—118no—
458C4⋊C8C22×D1114yes—
459#103—112no—
460#103—112no—
461#103C22×D1118yes—
462#102—112no—
463#102—118no—
464#102—112no—
465#97—114no—
466C4×C8—114no—
467C4×C8—112no—
468C4×C8—112no—
469C2×C11—22no—
470C2×C11—81no—
471C2×C11C2×#55011yescharacteristic
472C2×C11C2×#57712yes—
473D11—81no—
474D11—84no—
475C24—222no—
476#41—22no—
477#41—22no—
478#41—222no—
479#41—222no—
480#41—888no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—114no—
485C2×Q8—111no—
486C2×Q8C23×D1111yescharacteristic
487C2×Q8C23×D1114yes—
488C2×D4—21no—
489C2×D4—111no—
490C2×D4—114no—
491C2×D4—228no—
492C2×D4—221no—
493C2×D4—222no—
494C2×D4—224no—
495C2×D4—224no—
496C2×D4—224no—
497C2×D4—224no—
498C2×D4—884no—
499C2×D4C23×D1111yescharacteristic
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—228no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4D4×D1112yes—
507C22×C4C23×D1111yescharacteristic
508Q16—44no—
509Q16—222no—
510SD16—44no—
511SD16—222no—
512SD16—228no—
513SD16—228no—
514SD16—222no—
515SD16—444no—
516SD16—448no—
517D8—222no—
518D8—444no—
519M16—24no—
520C2×C8—114no—
521C2×C8—111no—
522C2×C8—111no—
523C2×C8—112no—
524C2×C8—222no—
525C2×C8C23×D1114yes—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—114no—
530C4⋊C4—114no—
531C4⋊C4—118no—
532C4⋊C4—112no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C4⋊C4—222no—
536C4⋊C4C23×D1112yes—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—114no—
540C22⋊C4—228no—
541C22⋊C4—228no—
542C22⋊C4—228no—
543C22⋊C4—221no—
544C22⋊C4—222no—
545C42—21no—
546C42—22no—
547C42—114no—
548C42—228no—
549C42—221no—
550C42—222no—
551C42D4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42C23×D1112yes—
554C11#6141011yescharacteristic, complemented, Sylow
555C23—21no—
556C23—221no—
557C23—224no—
558C23—444no—
559C23—884no—
560C23C2×D4×D1111yescharacteristic
561Q8—24no—
562Q8—21no—
563Q8—24no—
564Q8—21no—
565Q8—44no—
566Q8—228no—
567Q8—221no—
568Q8—221no—
569D4—21no—
570D4—21no—
571D4—42no—
572D4—221no—
573D4—224no—
574D4—221no—
575D4—224no—
576D4—442no—
577D4—448no—
578D4—444no—
579D4—884no—
580D4—888no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—24no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—42no—
588C2×C4—118no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—444no—
592C2×C4—442no—
593C2×C4—888no—
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1112yes—
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4#6703712yes—
598C2×C4#41×D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—24no—
601C8—112no—
602C8—112no—
603C8—222no—
604C22—22no—
605C22—41no—
606C22—42no—
607C22—441no—
608C22—444no—
609C22—442no—
610C22—448no—
611C22—1764no—
612C22#1062313012yes—
613C22C22×D4×D1111yescharacteristic
614C4—22no—
615C4—41no—
616C4—44no—
617C4—42no—
618C4—228no—
619C4—441no—
620C4—442no—
621C4#1062313012yes—
622C4#1062330914yes—
623C4C2×#6703711yescharacteristic
624C4C2×#41×D1111yescharacteristic
625C2—22no—
626C2—81no—
627C2—884no—
628C2—881no—
629C2C2×#1062313011yescharacteristic
630C2C2×#1062330912yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3039C2
socleC22×C11C23×D4
hypercenter#3039D11
hypocenterC11#61410
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082500C2semidirect
2. #13082492C2semidirect
3. #13081673C2semidirect
4. #13081635C2semidirect
5. #13081611C2semidirect
6. #13081592C2semidirect
7. #13079095C2semidirect
8. C2×#10622698C2semidirect
9. #13078139C2semidirect
10. #13078127C2semidirect
11. #13078097C2semidirect
12. #13077546C2semidirect
13. #13077471C2semidirect
14. C4×#67003C2semidirect
15. C11×#3039C2semidirect
26. #10623263C22semidirect
29. #10623252C22semidirect
40. C11×#462C22semidirect
41. C11×#461C22semidirect
45. #10622804C22semidirect
46. #10622803C22semidirect
47. #10622798C22semidirect
48. #10622789C22semidirect
49. #10622788C22semidirect
50. #10622776C22semidirect
56. C4×#4326C22semidirect
57. C4×#4325C22semidirect
58. C4×#4324C22semidirect
59. C4×#4323C22semidirect
65. #10622444C22semidirect
66. #10622443C22semidirect
67. #10622432C22semidirect
68. #10622431C22semidirect
69. #10622430C22semidirect
70. #10622401C22semidirect
234. C2×C11⋊C8#41semidirect
250. #3039D11semidirect
336. #462C2×D11semidirect
338. #461C2×D11semidirect
554. C11#61410semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130825002
#130824922
#130816732
#130816352
#130816112
#130815922
#130790952
C2×#106226982
#130781392
#130781272
#130780972
#130775462
#130774712
C4×#670032
C11×#30392
#6141011